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Test of Non-linearity of a Time Series

Source: R/nonlintest.R
nonlintest.Rd

A bootstrap test of non-linearity in a time series using the third-order moment.

Usage

nonlintest(data, n.lag, n.boot, alpha = 0.05)

Arguments

data

a vector of equally spaced numeric observations (time series).

n.lag

the number of lags tested using the third-order moment, maximum = length of time series.

n.boot

the number of bootstrap replications (suggested minimum of 100; 1000 or more would be better).

alpha

statistical significance level of test (default=0.05).

Value

Returns an object of class "nonlintest" with the following parts:

  • region: the region of the third order moment where the test exceeds the limits (up to n.lag).

  • n.lag: the maximum lag tested using the third-order moment.

  • stats: a list of statistics for the area outside the test limits:

    • outside: the total area outside of limits (summed over the whole third-order moment).

    • stan: the total area outside the limits divided by its standard deviation to give a standardised estimate.

    • median: the median area outside the test limits.

    • upper: the (1-alpha)th percentile of the area outside the limits.

    • pvalue: bootstrap p-value of the area outside the limits to test if the series is linear.

    • test: reject the null hypothesis that the series is linear (TRUE/FALSE).

Details

The test uses aaft to create linear surrogates with the same second-order properties, but no (third-order) non-linearity. The third-order moments (third) of these linear surrogates and the actual series are then compared from lags 0 up to n.lag (excluding the skew at the co-ordinates (0,0)). The bootstrap test works on the overall area outside the limits, and gives an indication of the overall non-linearity. The plot using region shows those co-ordinates of the third order moment that exceed the null hypothesis limits, and can be a useful clue for guessing the type of non-linearity. For example, a large value at the co-ordinates (0,1) might be caused by a bi-linear series \(X_t=\alpha X_{t-1}\varepsilon_{t-1} +\varepsilon_t\).

References

Barnett AG & Wolff RC (2005) A Time-Domain Test for Some Types of Nonlinearity, IEEE Transactions on Signal Processing, vol 53, pages 26–33 doi: 10.1109/TSP.2004.838942 .

See also

print.nonlintest() plot.nonlintest()

Author

Adrian Barnett a.barnett@qut.edu.au

Examples

# \donttest{
if (FALSE) { # \dontrun{
test_res <- nonlintest(data = CVD$cvd, n.lag = 4, n.boot = 1000)
} # }
# }